Two Definitions of Superfluid Density

TL;DR

This paper clarifies that two common definitions of superfluid density differ in dimensions less than three due to underlying statistical physics, with implications for experimental observations.

Contribution

It identifies and explains the fundamental difference between static and dynamic definitions of superfluid density in lower dimensions, highlighting their physical origins.

Findings

Static and dynamic superfluid densities generally differ in <3D.

The difference arises from equilibrium supercurrent statistics.

Experimental consequences of this difference are discussed.

Abstract

We point out that two different definitions of the superfluid density - through statistical response to static gauge phase and through dynamic response to altering gauge phase - yield, generally speaking, different quantities in $d<3$. The physics leading to this difference is associated with the equilibrium statistics of supercurrent states. Some experimentally observable consequences of this fact are discussed.